Manim(3B1B style) Videos for Students

[InigoMontoya314]

Portfolio

Sample video made by us:

https://youtu.be/4gX0trYrjPA

https://www.youtube.com/watch?v=Dzw1pJuPAzs

Target topic categories

Anything mathematical that is approachable for high schoolers, but not just restricted to high school math classes. Things like basic multivariable calculus, analysis, linear algebra, number theory are welcomed, as one of us have an introductory background in those subjects(I'm not trained in such fields as a high school senior, though I get the basic notions and ideas). We also have background in error-correcting codes. However, with that said as a curious student I'm happy to explore new areas that are within my mathematical capability.

We also welcome topics in computer science that are adequate for, but not restricted to, high schoolers. Topics such as logic gates, elementary circuit designs, algorithm analysis (searching, dynamic programming, sorting), and neural networks, programming languages (python, C/C++) are preferred. Still, we are also open to exploring new areas!

Target medium

Manim Video. We taught ourselves manim for a school project and then absolutely loved it. See the portfolio above for sample videos from each of us.

Contact details

Github is fine for now, but if you are interested in making a video with me then we can talk a bit more using email and stuff like that.

Additional context

We are two seniors who just graduated from high school and will respectively major in math and computer science at university. As we are bored for the summer, we want to work on something fun and decide to pick up manim to do a few projects. You can expect more mathematical and computer science background from us than a normal high schooler, also we have experience in mathematical and computer science teaching(one of us taught summer schools before, coached math teams, and even helped my school develop assessments for middle schoolers, another runs programming algorithm club and taught computer science to autism groups)   We are far from professional in terms of animation and video editing, so if you are looking for a professional content creator then unfortunately we can't help. We are not particularly good with video and audio editing either. However, if you struggle with making mathematics/computer science concepts accessible to undergrads/high schoolers/middle schoolers/general audience(say, you are a math/cs teacher/professor and want some animations for your class), then we are the right group to find, as we can see from the perspective of the students and help explain stuff in an easier manner.   Pay: we don't care about pay. We'll appreciate it if you want to pay us, and it's completely fine if you don't. All we are up to is to make some cool animations, do something meaningful and (possibly) learn some new math/cs.   Time: Unfortunately the university term starts in September, so we'd prefer to have everything done ideally at the end of August. However, that still leaves us plenty of time to get a great project done!

[FAUM]

Hello, I really liked the animation style in your video! I also think you lie right in my target audience of interested high school/college level math with a taste for 'aha' moments.

If you're interested, I have a plan for a project that involves linear algebra in a rather non-traditional way to characterize fractals. Essentially, the eigenvalues of a matrix tell us the fractal dimension, and the eigenvectors tell us the ratio of red:blue:green pixels in the fractal image, which comes as a nice surprise. There are other 'aha' moments as well, such as figuring out how to interpret complex eigenvalues. I wrote up some more of the details in #52 if you want to check it out.

[RandomCitizen21]

Hi. That's a nice video.

I'm a student who just got my undergraduate degree in math, and I've got an idea for an exciting video. In 3B1B's video on eigenvectors, he covers the basic idea of vectors that stay on their span during a transformation and how to diagonalize a matrix. However, he mainly covers real and diagonalizable matrices, whereas the full theory of eigenvectors applies to many more transformations. There is a variation called Jordan-diagonalization which can be done to any matrix (even those without enough eigenvectors).

To motivate this concept, we could consider a vector v(t) that depends on time t and satisfies v'(t)=Mv(t), where M is a matrix. The solution to this problem is very understandable if M is diagonalizable. (Form the matrix e^(Mt) (it has the same eigenvectors as M, but the eigenvalues are e^(λt) instead of λ), and multiply it by v(0) (v(t) at time t=0)) However, if M is not diagonalizable, then understanding generalized eigenvectors is required to proceed.

I was thinking of covering: Complex eigenvalues and eigenvectors (there are some nice animations and 'a-ha' moments here) Generalized eigenvectors and Jordan-block matrices (the key to our problem) A quick proof that every matrix can be Jordan-diagonalized (yes, all of them) And, to conclude the video, how to solve v'(t)=Mv(t).

[kingking1223]

Hello, I am very impressed with your work. My video plan is #121 so please check it and reply me if you are interested. You may contact me by replying to this comment or sending a message to a me through discord. My discord account is kingking#5776. Yours faithfully, King 10:52 12 Jun 2022

[rudrathegreat]

Hello hello! my name is Rudra, I'm a high school student from Australia and I think one topic that many of my friends struggle with is the idea of how composite functions work. I was thinking we could do a collab on helping high schoolers understand how composite functions, some of the properties and checking for the existence of composite functions. For more info about my video idea, check out the issue #138. My email is rudrasekhri@gmail.com

[rudrathegreat]

I'm definitely not an expert, but I think I might have a way to explain the idea of composite functions using ducks and duck-eating dragons!!!

[cycloconverter-guru]

Hi,

My name is Michael Harrison. I am a Power Electronics Engineer and I have an idea for creating a video that explains a very complex Power Systems theory into Symmetrical Components in a way that is very simple to understand and will have appeal to a very wide audience. Take a look at my idea #146 and contact me if you are interested in knowing more about this topic.

[aargup934]

Hi, I would like to put up my idea at #18, it would include stuff like Graph theory and Ramsey theory where animations would be quite useful. I may not be an expert, but I hope you consider my idea for a collab

[electrineer1]

Hello

I'm also looking to make a video about symmetrical components post #173, however my storyboard explores a different area of this topic than cycloconverter's lesson mentioned above. It's possible some combined efforts here may give you the animations you need to make two videos about this topic, one for each of us.

My email is nategk88@gmail.com. Please let me know if you're interested.

Nathan Kassees

[brainandforce]

Hi there! I've made post #201 and while it may be a bit beyond the scope of the math you mentioned here, I could definitely use someone who can help animate classical and quantum physics!